{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:64D4H4A35BB5VR4QBZRO4D6O7S","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5a12c517edb63f5f133d3682639eced8dd558be4014eec9951af89fababe11b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-10-09T02:53:20Z","title_canon_sha256":"44cfecaa25467dc6cf59929ffd63b1ab8623afdfb5a4c0a084624c0161629c76"},"schema_version":"1.0","source":{"id":"1710.02920","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.02920","created_at":"2026-05-18T00:33:28Z"},{"alias_kind":"arxiv_version","alias_value":"1710.02920v1","created_at":"2026-05-18T00:33:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.02920","created_at":"2026-05-18T00:33:28Z"},{"alias_kind":"pith_short_12","alias_value":"64D4H4A35BB5","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"64D4H4A35BB5VR4Q","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"64D4H4A3","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:203159beaa44090acb43fb2a08b164bdfb3f4ccc5c6fee5267076a342b1e30cf","target":"graph","created_at":"2026-05-18T00:33:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove a version of a small index property theorem for strong amalgamation classes. Our result builds on an earlier theorem by Lascar and Shelah (in their case, for saturated models of uncountable first-order theories). We then study versions of the small index property for various non-elementary classes. In particular, we obtain the small index property for quasiminimal pregeometry structures.","authors_text":"Andr\\'es Villaveces, Zaniar Ghadernezhad","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-10-09T02:53:20Z","title":"The small index property for homogeneous models in AECs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02920","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:adc8d61139ae5c386c62dc3899a7cb5703d7d186d2df8a0453da16b473968ce3","target":"record","created_at":"2026-05-18T00:33:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5a12c517edb63f5f133d3682639eced8dd558be4014eec9951af89fababe11b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-10-09T02:53:20Z","title_canon_sha256":"44cfecaa25467dc6cf59929ffd63b1ab8623afdfb5a4c0a084624c0161629c76"},"schema_version":"1.0","source":{"id":"1710.02920","kind":"arxiv","version":1}},"canonical_sha256":"f707c3f01be843dac7900e62ee0fcefcb037aab61e7526acae1b7572686c481f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f707c3f01be843dac7900e62ee0fcefcb037aab61e7526acae1b7572686c481f","first_computed_at":"2026-05-18T00:33:28.454581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:28.454581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ls6tUTdDtKBFfRM7uRcUaH8mob9bnHIHjZuc+PIM2qbMns3qPSMjhZuGzpIdRzv1pdUjvr4Aiyj5/jmY1zfMDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:28.455105Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.02920","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adc8d61139ae5c386c62dc3899a7cb5703d7d186d2df8a0453da16b473968ce3","sha256:203159beaa44090acb43fb2a08b164bdfb3f4ccc5c6fee5267076a342b1e30cf"],"state_sha256":"3cfbcd6cf679ff0315cdf90f647a0fab034fc78360f402ef58719a36260b130c"}